Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Suppose that [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are sets, defined as follows. Find the intersection and union of [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. Enter the elements of the sets in increasing order, separated by commas. If a set is the empty set, just enter DNE inside the braces given.

[tex]\[
\begin{array}{l}
A = \{2, 3, 6, 7\} \text{ and } B = \{1, 2, 3, 6, 7, 8\} \\
A \cap B = \{\square\} \\
A \cup B = \{\square\}
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Given the sets [tex]\( A = \{2, 3, 6, 7\} \)[/tex] and [tex]\( B = \{1, 2, 3, 6, 7, 8\} \)[/tex], we need to determine the intersection and union of these sets.

### Intersection ([tex]\(A \cap B\)[/tex]):
The intersection of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are common to both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

The common elements are [tex]\( 2, 3, 6, \)[/tex] and [tex]\( 7 \)[/tex].

Thus, the intersection [tex]\(A \cap B = \{2, 3, 6, 7\}\)[/tex].

### Union ([tex]\(A \cup B\)[/tex]):
The union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are in [tex]\( A \)[/tex], in [tex]\( B \)[/tex], or in both.
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

Combining the elements from both sets (and removing duplicates) gives us: [tex]\( 1, 2, 3, 6, 7, \)[/tex] and [tex]\( 8 \)[/tex].

Thus, the union [tex]\(A \cup B = \{1, 2, 3, 6, 7, 8\}\)[/tex].

### Answer:
[tex]\[ \begin{array}{l} A = \{2, 3, 6, 7\} \\ B = \{1, 2, 3, 6, 7, 8\} \\ A \cap B = \{2, 3, 6, 7\} \\ A \cup B = \{1, 2, 3, 6, 7, 8\} \end{array} \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.